A firm that purchases electricity from the local utility is considering installing a steam generator. A large generator costs $290,000 whereas a small generator costs $170,000. The cost of operating the generator would be $300,000 per year for the large and $320,000 for the small. Either generator will last for five years. The cost of capital is 11%.

For each generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year (i.e., immediate, one year from now,..., four years from now).

**What is the net present value of the more attractive generator?**

To determine the net present value (NPV) of the more attractive generator, we need to compare the NPVs of the two options:

1. **Large Generator:**
   - Initial Cost: $ \$290,000 $
   - Annual Operating Cost: $ \$300,000 $ for 5 years

2. **Small Generator:**
   - Initial Cost: $ \$170,000 $
   - Annual Operating Cost: $ \$320,000 $ for 5 years

The NPV for each generator is the sum of the initial cost and the present value of the operating costs over the 5 years.

The formula for the present value (PV) of an annuity is:

\[
PV_{\text{annuity}} = C \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)
\]

Where:
- $ C $ = Annual operating cost
- $ r $ = Cost of capital (11% or 0.11)
- $ n $ = Number of years (5 years)

The total present value (including the initial cost) for each generator is:

\[
PV_{\text{total}} = \text{Initial Cost} + PV_{\text{annuity}}
\]

### 1. **Present Value of Costs for the Large Generator:**

\[
PV_{\text{large}} = 290,000 + \left(300,000 \times \left(\frac{1 - (1 + 0.11)^{-5}}{0.11}\right)\right)
\]

### 2. **Present Value of Costs for the Small Generator:**

\[
PV_{\text{small}} = 170,000 + \left(320,000 \times \left(\frac{1 - (1 + 0.11)^{-5}}{0.11}\right)\right)
\]

Let's calculate these values.The present value of the costs for the two generator options are as follows:

1. **Large Generator:** $ PV_{\text{large}} $ = $-\$1,398,769$
2. **Small Generator:** $ PV_{\text{small}} $ = $-\$1,352,687$

Since the small generator has a lower present value of costs, it is the more attractive option.

### **Net Present Value (NPV) of the More Attractive Generator:**

The NPV of the more attractive generator (the small generator) is $-\$1,352,687$.

Would you like more details or have any questions? Here are some related questions that might interest you:

1. How does the cost of capital influence the NPV in these scenarios?
2. What factors could justify choosing the large generator despite its higher NPV?
3. How would changes in operating costs affect the decision?
4. What impact would a longer generator lifespan have on the NPV?
5. How can the firm assess the risk associated with these investments?

**Tip:** In capital budgeting decisions, it's important to consider not only the NPV but also other factors like operational risks and potential changes in future costs.

Learn how to calculate the net present value (NPV) for a large generator costing $290,000 with $300,000 annual operating cost and a small generator costing $170,000 with $320,000 annual operating cost over 5 years at 11% cost of capital. Understand the financial implications and decision-making criteria between the two options.

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